options(tz="America/New_York")
Sys.setenv(TZ="America/New_York")

1 Data Collection

1.1 Benchmark data

Risk-free Rates

tbill <- vroom("https://fred.stlouisfed.org/graph/fredgraph.csv?bgcolor=%23e1e9f0&chart_type=line&drp=0&fo=open%20sans&graph_bgcolor=%23ffffff&height=450&mode=fred&recession_bars=on&txtcolor=%23444444&ts=12&tts=12&width=1168&nt=0&thu=0&trc=0&show_legend=yes&show_axis_titles=yes&show_tooltip=yes&id=DTB3&scale=left&cosd=2009-08-01&coed=2020-10-09&line_color=%234572a7&link_values=false&line_style=solid&mark_type=none&mw=3&lw=2&ost=-99999&oet=99999&mma=0&fml=a&fq=Daily&fam=avg&fgst=lin&fgsnd=2020-02-01&line_index=1&transformation=lin&vintage_date=2020-10-14&revision_date=2020-10-14&nd=1954-01-04") %>%
  mutate(DTB3 = DTB3/100) %>%
  rename("date" = "DATE",
         "T_bill" = "DTB3") %>% 
  mutate(T_bill_d = (1 + T_bill)^(1/252)-1,
         date = as.Date(date,"%Y-%m-%d"))

Indices

benchmark <- 
  data.frame(index = c("MNA", "^RUA", "^FTSE","^FTAS", "^IXIC","NYA", "^DJI", "^GSPC"),
             description = c("IQ Merger Arbitrage ETF", "Russell_3000", "FTSE 100", "FTSE All Share","NASDAQ_Composite", "NYSE Composite", "Dow Jones Industrial Average", "SP_500")) %>% 
  tq_get(get  = "stock.prices",
         from = "2009-01-01",
         to   = "2020-08-31") %>%
  select(index, description, date, close) %>%
  group_by(index) %>%
  mutate(index_return = close/lag(close) - 1)

1.2 Merger Data

Merger Deals

stocks2 <- read_excel("MA_vF.xlsx", sheet = "Sheet1") %>% 
  select(acquirer, target, DealStatus, announce_date, close_date) %>%
  mutate(DealStatus = case_when(
    DealStatus == "Completed" ~ DealStatus,
    TRUE ~ "Failed"),
    DealID = paste(acquirer,target))

1.3 Get Stock Data and build Dataframes

1.3.1 Acquirer Data

acquirer_raw <- stocks2 %>%
  select(acquirer) %>% 
  tq_get(get  = "stock.prices",
         from = "2009-01-01",
         to   = "2020-08-31") %>%
  select(date, acquirer, open, close)

1.3.2 Target Data

target_raw <- stocks2 %>% 
  select(target) %>% 
  tq_get(get  = "stock.prices",
         from = "2009-01-01",
         to   = "2020-08-31") %>%
  select(date, target, open, close)

1.3.3 Reformat

# Reformat acquirer data
stock_data_acquirer <- acquirer_raw %>%
  group_by(acquirer) %>% 
  mutate(close_acquirer = sprintf("%.2f", open, na.rm = TRUE)) %>%
  select(acquirer, date, close_acquirer)
# Reformat target data
stock_data_target <- target_raw %>%
  group_by(target) %>% 
  mutate(close_target = sprintf("%.2f", open, na.rm = TRUE)) %>%
  select(target, date, close_target)

2 Trade from 1 day past announcement date

acq_tar <- stocks2 %>%
  
  #Add acquirer data
  left_join(stock_data_acquirer, by = c("acquirer")) %>%
  distinct(DealID, date, .keep_all = T) %>% 
  mutate(announce_date = as.Date(announce_date,"%Y-%m-%d", tz = "America/New_York"),
         close_date = as.Date(close_date,"%Y-%m-%d", tz = "America/New_York"),
         standard_date = date - announce_date,
         standard_date2 = lead(standard_date, n = 2L)) %>% 
  group_by(DealID) %>% 
  filter(standard_date >= -2,
         date <= close_date) %>% 
  mutate(period = row_number(),
         period = period + as.numeric(time_length( min(standard_date), "days")) -2 ) %>% 
 
  # Add target data
  left_join(stock_data_target, by = c("target", "date")) %>%
  drop_na(close_target) %>%
  
  # Add Acquirer Returns
  group_by(DealID) %>%
  mutate(close_acquirer = as.numeric(close_acquirer, na.rm = TRUE),
    ret_acq = ifelse(period < 0, NA, ifelse(period > 0, close_acquirer/lag(close_acquirer) - 1, 0))) %>%
  
  # Add target Returns
  group_by(DealID) %>%
  mutate(close_target = as.numeric(close_target, na.rm = TRUE),
    ret_tar = ifelse(period < 0, NA, ifelse(period > 0, close_target/lag(close_target) - 1, 0))) %>%
  
  # Add combined returns
  
  mutate(ret_combined =  ifelse(is.na(ret_tar),NA, ifelse(is.na(ret_acq),NA, ret_tar - ret_acq))) %>% 
  # mutate(ret_combined = ifelse(DealStatus == "Completed", ret_tar - ret_acq,  ret_acq - ret_tar)) %>% # If predict deal succeeds vs predict deal fails, assuming 100% predictive capabilities - CAN CHANGE
  # Get rid of non-sense returns
  filter(!is.infinite(ret_combined))

2.1 Daily Return and Acquirer - Target Spread

acq_tar %>%
  group_by(period) %>%
  # Summarise means per period whilst removing all NAs. Bad data quality forces us to do this
  summarise(mean_acq = mean(ret_acq, na.rm = TRUE),
            mean_tar = mean(ret_tar, na.rm = TRUE),
            mean_strat = mean(ret_combined, na.rm = TRUE)) %>%
  filter(period <= 50) %>%
  ggplot() +
  theme_bw() +
  geom_line(aes(x = period, y = (mean_acq)), colour = "red") + # Acquirer return
  geom_line(aes(x = period, y = (mean_tar)), colour = "blue") + # Target return

  labs(title = "Return spread between Target and Acquirer narrows quickly",
       subtitle = "Mean Daily Returns of Targets and Acquirers per Day from Announcement",
       y = "Daily Returns",
       x = "Day from initial announcement") + 
  theme_economist_white()

ggsave("Return Spread Target an Acquirer.png",
       plot = last_plot(),
       scale = 1,
       width = 20,
       height = 15,
       units = "cm",
       dpi = 300,
       limitsize = TRUE)

knitr::include_graphics(here::here("Return Spread Target an Acquirer.png"), error = FALSE)

acq_tar %>%
  group_by(period) %>%
  # Summarise means per period whilst removing all NAs. Bad data quality forces us to do this
  summarise(mean_acq = mean(ret_acq, na.rm = TRUE),
            mean_tar = mean(ret_tar, na.rm = TRUE),
            mean_strat = mean(ret_combined, na.rm = TRUE)) %>%
  filter(period <= 50) %>%
  ggplot() +
  theme_bw() +
  geom_line(aes(x = period, y = (mean_strat)), colour = "green") + # Portfolio 
  labs(title = "Target and Acquirer Spread drives Strategy Return",
       subtitle = "Mean Daily Returns of Strategy per Day from Announcement",
       y = "Daily Returns",
       x = "Day from initial announcement") + 
  theme_economist_white()

ggsave("Strategy Return from Spread.png",
       plot = last_plot(),
       scale = 1,
       width = 20,
       height = 15,
       units = "cm",
       dpi = 300,
       limitsize = TRUE)

knitr::include_graphics(here::here("Strategy Return from Spread.png"), error = FALSE)

2.2 Cumulative Return

2.2.1 Acquirer

# Cumulative return for acquirer
initial_acq <- acq_tar %>%
  filter(period == 0) %>%
  rename(initial_acq = close_acquirer) %>%
  select(acquirer, target, initial_acq) %>%
  distinct()

cum_acq <- left_join(acq_tar, initial_acq, by = c("acquirer", "target")) %>%
  mutate(cum_ret_acq = ifelse(period > -1, close_acquirer/initial_acq - 1, NA)) %>%
  group_by(period) %>%
  summarise(mean_cum_ret_acq = mean(cum_ret_acq, na.rm =TRUE)) %>%
  filter(period <= 50)

2.2.2 Target

# Cumulative return for target
initial_tar <- acq_tar %>%
  filter(period == 0) %>%
  rename(initial_tar = close_target) %>%
  select(acquirer, target, initial_tar) %>% 
  distinct()

cum_tar <- left_join(acq_tar, initial_tar, by = c("acquirer", "target")) %>%
  mutate(cum_ret_tar = ifelse(period > -1, close_target/initial_tar - 1, NA)) %>%
  group_by(period) %>%
  summarise(mean_cum_ret_tar = mean(cum_ret_tar, na.rm =TRUE)) %>%
  filter(period <= 50)

2.2.3 Cumulative Return Spread

# Combine all
cum_all <- left_join(cum_acq, cum_tar, by = "period") %>%
  filter(period <= 50)
  

ggplot(cum_all) +
  
  geom_line(aes(x = period, y = mean_cum_ret_tar), colour = "blue") +
  geom_line(aes(x = period, y = mean_cum_ret_acq), colour = "red") +
  theme_bw() +
  labs(subtitle = "Mean Cumulative Return - Investments start 1 day after announcement",
       title = "Target outperformance in cumulative return driven by early gains",
       y = "Cumulative Return",
       x = "Day from announcement") + 
  theme_economist_white()

ggsave("Cumulative Returns Target and Acquirer.png",
       plot = last_plot(),
       scale = 1,
       width = 20,
       height = 15,
       units = "cm",
       dpi = 300,
       limitsize = TRUE)

knitr::include_graphics(here::here("Cumulative Returns Target and Acquirer.png"), error = FALSE)

2.3 Correlation between return and deal completion

2.3.1 Acquirer

end_acq <- acq_tar %>%
  mutate(diff = close_date - date) %>%
  filter(diff == 0) %>%
  rename(end_acq = close_acquirer) %>%
  select(acquirer, period, target, end_acq, DealStatus) %>%
  distinct()


deal_ret_acq <- left_join(end_acq, initial_acq, by = c("acquirer", "target")) %>% 
  distinct() %>%
  mutate(annualised_ret = (end_acq/initial_acq)^(252/period) - 1) %>%
  group_by(DealStatus) %>%
  summarise(mean_annualised_acq_ret = median(annualised_ret, na.rm = TRUE))

deal_ret_acq

DealStatusmean_annualised_acq_ret
Completed-0.0129
Failed-0.46  
### Target

end_tar <- acq_tar %>%
  mutate(diff = close_date - date) %>%
  filter(diff == 0) %>%
  rename(end_tar = close_target) %>%
  select(acquirer, period, target, end_tar, DealStatus) %>%
  distinct()


deal_ret_tar <- left_join(end_tar, initial_tar, by = c("acquirer", "target")) %>%
  filter(!is.na(end_tar)) %>%
  mutate(annualised_ret = (end_tar/initial_tar)^(252/period) - 1) %>%
  group_by(DealStatus) %>%
  summarise(mean_annualised_tar_ret = sprintf("%.2f",median(annualised_ret, na.rm = TRUE)))

deal_ret_tar
DealStatusmean_annualised_tar_ret
Completed0.09
Failed-0.17

Huge failed deal target return driven by T - STRP deal, where STRP’s stock increased by 150% in 20 days.

2.4 Returns of strategy over timeline

2.4.1 S&P 500 is no deal

acq_tar2 <- acq_tar %>%
  filter(period <= 50) %>% 
  group_by(date) %>%
  summarise(ret_strat = mean(ret_combined)) %>% 
  filter(!is.na(ret_strat))




SP_initial <- benchmark %>%
  filter(description == "SP_500") %>%
  filter(date >= "2015-01-01") %>%
  arrange(date) %>%
  head(n = 1) %>%
  rename(initial_index = close) %>%
  select(- date, - index_return)

  ggplot(acq_tar2) +
  geom_line(aes(x = date, y = ret_strat), colour = "red") 

benchmark %>%
  filter(description == "SP_500") %>%
  arrange(date) %>%
  left_join(SP_initial, by = c("description", "index")) %>%
  left_join(acq_tar2, by = "date") %>%
  select(date, close, initial_index, ret_strat) %>%
  mutate(index_ret = close/lag(close) - 1,
         cum_index_ret = close/initial_index,
         ret_strat_adjusted = ifelse(is.na(ret_strat), index_ret, ret_strat)) %>%
  filter(date >= "2015-01-01") %>%
  mutate(retplus1 = ret_strat_adjusted + 1,
    cum_ret_strat = cumprod(retplus1)) %>%
  ggplot() +
  geom_line(aes(x = date, y = cum_index_ret), colour = "red") +
  geom_line(aes(x = date, y = cum_ret_strat), colour = "green") +
  labs(subtitle = "Cumulative Return Strategy vs Index",
       title = "Perfect Foresight Generates Above Market Returns",
       y = "Cumulative Return",
       x = "Day from initial investment") + 
  theme_economist_white()

ggsave("Cumulative Return Strategy vs Index.png",
       plot = last_plot(),
       scale = 1,
       width = 20,
       height = 15,
       units = "cm",
       dpi = 300,
       limitsize = TRUE)

knitr::include_graphics(here::here("Cumulative Return Strategy vs Index.png"), error = FALSE)

### Risk free if no deal

benchmark %>%
  filter(description == "SP_500") %>%
  arrange(date) %>%
  left_join(SP_initial, by = c("description", "index")) %>%
  left_join(acq_tar2, by = "date") %>%
  left_join(tbill, by = "date") %>%
  select(date, close, initial_index, ret_strat, T_bill_d) %>%
  mutate(index_ret = close/lag(close) - 1,
         cum_index_ret = close/initial_index,
         ret_strat_adjusted = ifelse(is.na(ret_strat), T_bill_d, ret_strat)) %>%
  filter(date >= "2014-05-01") %>%
  mutate(retplus1 = ret_strat_adjusted + 1,
    cum_ret_strat = cumprod(retplus1)) %>%
  ggplot() +
  geom_line(aes(x = date, y = cum_index_ret), colour = "red") +
  geom_line(aes(x = date, y = cum_ret_strat), colour = "green") +
  labs(subtitle = "Cumulative Return Strategy vs Index",
       title = "Perfect Foresight Generates Above Market Returns",
       y = "Cumulative Return",
       x = "Day from initial investment") + 
  theme_economist_white()

2.5 CAPM

benchmarkSP <- benchmark %>%
  filter(description == "SP_500") %>%
  pivot_wider(values_from = index_return, names_from = description) %>%
  select(date, SP_500)


CAPM <- acq_tar %>%
  filter(period <= 20) %>% 
  left_join(tbill, by = "date") %>%
  left_join(benchmarkSP, by = "date") %>% 
  filter(!is.na(ret_combined)) %>% 
  mutate(Rm_Rf = SP_500 - T_bill_d,
         Rs_Rf = ret_combined - T_bill_d) %>%  # CAN MUTATE RET_Strat = S&P/TBill if return = NA, then use that to replace ret_combined here
  drop_na(Rm_Rf, Rs_Rf) %>%
  filter(!is.infinite(Rs_Rf))

ggplot(CAPM, aes(x = Rm_Rf, y = Rs_Rf, na.rm = TRUE)) +
  geom_point() +
  geom_smooth(method = lm)  +
  ylim(-1,1) +
  labs(subtitle = "Excess Returns of Startegy vs Market Benchmark (scale ignoring 2 outliers)",
       title = "Regression shows minimal positive Alpha and Beta for daily returns",
       y = "Excess Return Strategy",
       x = "Excess Return Benchmark") + 
  theme_economist_white()

ggsave("Excess Returns of Startegy vs Market Benchmark.png",
       plot = last_plot(),
       scale = 1,
       width = 25,
       height = 15,
       units = "cm",
       dpi = 300,
       limitsize = TRUE)

knitr::include_graphics(here::here("Excess Returns of Startegy vs Market Benchmark.png"), error = FALSE)

CAPM_regression <- lm(Rs_Rf ~ Rm_Rf, data = CAPM, na.rm =TRUE)

CAPM_regression
## 
## Call:
## lm(formula = Rs_Rf ~ Rm_Rf, data = CAPM, na.rm = TRUE)
## 
## Coefficients:
## (Intercept)        Rm_Rf  
##    0.005822     0.000526
huxreg(CAPM_regression,
       statistics = c('#observations' = 'nobs', 
                      'R squared' = 'r.squared', 
                      'Adj. R Squared' = 'adj.r.squared', 
                      'Residual SE' = 'sigma'), 
       bold_signif = 0.05, 
       stars = NULL
)
(1)
(Intercept)0.006 
(0.003)
Rm_Rf0.001 
(0.311)
#observations2213     
R squared0.000 
Adj. R Squared-0.000 
Residual SE0.139 
msummary(CAPM_regression)
##             Estimate Std. Error t value Pr(>|t|)  
## (Intercept) 0.005822   0.002950    1.97    0.049 *
## Rm_Rf       0.000526   0.311403    0.00    0.999  
## 
## Residual standard error: 0.139 on 2211 degrees of freedom
## Multiple R-squared:  1.29e-09,   Adjusted R-squared:  -0.000452 
## F-statistic: 2.85e-06 on 1 and 2211 DF,  p-value: 0.999

—– END OF ANALYSIS USED IN PAPER ——–

2.5.1 Unsused Calculations

The remainder of this document are conducted analyses that were chosen not to report on in the project.

TRADE AFTER ANNOUNCEMENT DATE - SHOULD USE CLOSING PRICES HERE

# Reformat acquirer data
stock_data_acquirer_v2 <- acquirer_raw %>%
  group_by(acquirer) %>% 
  mutate(close_acquirer = sprintf("%.2f", close, na.rm = TRUE)) %>%
  select(acquirer, date, close_acquirer)
# Reformat target data
stock_data_target_v2 <- target_raw %>%
  group_by(target) %>% 
  mutate(close_target = sprintf("%.2f", close, na.rm = TRUE)) %>%
  select(target, date, close_target)
acq_tar <- stocks2 %>%
  
  #Add acquirer data
  left_join(stock_data_acquirer, by = c("acquirer")) %>%
  distinct(DealID, date, .keep_all = T) %>% 
  mutate(announce_date = as.Date(announce_date,"%Y-%m-%d", tz = "America/New_York"),
         close_date = as.Date(close_date,"%Y-%m-%d", tz = "America/New_York"),
         standard_date = date - announce_date,
         standard_date2 = lead(standard_date, n = 2L)) %>% 
  group_by(DealID) %>% 
  filter(standard_date >= -2,
         date <= close_date) %>% 
  mutate(period = row_number(),
         period = period + as.numeric(time_length( min(standard_date), "days")) -1) %>% 

  left_join(stock_data_target, by = c("target", "date")) %>%
  drop_na(close_target) %>%

  group_by(DealID) %>%
  mutate(close_acquirer = as.numeric(close_acquirer, na.rm = TRUE),
    ret_acq = ifelse(period < 0, NA, ifelse(period > 0, close_acquirer/lag(close_acquirer) - 1, 0))) %>%
  
  group_by(DealID) %>%
  mutate(close_target = as.numeric(close_target, na.rm = TRUE),
    ret_tar = ifelse(period < 0, NA, ifelse(period > 0, close_target/lag(close_target) - 1, 0))) %>%
  
  
  mutate(ret_combined =  ret_tar - ret_acq) %>% 

  filter(!is.infinite(ret_combined))


acq_tar_v2 <- stocks2 %>%
  
  #Add acquirer data
  left_join(stock_data_acquirer_v2, by = c("acquirer")) %>%
  distinct(DealID, date, .keep_all = T) %>% 
  mutate(announce_date = as.Date(announce_date,"%Y-%m-%d", tz = "America/New_York"),
         close_date = as.Date(close_date,"%Y-%m-%d", tz = "America/New_York"),
         standard_date = date - announce_date,
         standard_date2 = lead(standard_date, n = 2L)) %>% 
  group_by(DealID) %>% 
  filter(standard_date2 >= -2,
         date <= close_date) %>%
  # Add period number (by trading days)
  mutate(period = row_number(),
         period = period + as.numeric(time_length( min(standard_date), "days")) -1) %>% 
  
  # Add target data
  left_join(stock_data_target_v2, by = c("target", "date")) %>%
  drop_na(close_target) %>%
  
  # Add Acquirer Returns
  group_by(DealID) %>%
  mutate(close_acquirer = as.numeric(close_acquirer, na.rm = TRUE),
    ret_acq = ifelse(period < 0, NA, ifelse(period > 0, close_acquirer/lag(close_acquirer) - 1, 0))) %>%
  
  # Add target Returns
  group_by(DealID) %>%
  mutate(close_target = as.numeric(close_target, na.rm = TRUE),
    ret_tar = ifelse(period < 0, NA, ifelse(period > 0, close_target/lag(close_target) - 1, 0))) %>%
  
  # Add combined returns
  mutate(ret_combined =  ret_tar - ret_acq) %>% # If predict deal succeeds vs predict deal fails, assuming 100% predictive capabilities - CAN CHANGE
  
  filter(!is.infinite(ret_combined))

# acq_tar_v2 %>% filter(period == 0) %>% 
#   mutate(match = announce_date - date) %>% 
#   summarise(sum(match))

Daily Return

acq_tar_v2 %>%
  group_by(period) %>%
  # Summarise means per period whilst removing all NAs. Bad data quality forces us to do this
  summarise(mean_acq = mean(ret_acq, na.rm = TRUE),
            mean_tar = mean(ret_tar, na.rm = TRUE),
            mean_strat = mean(ret_combined, na.rm = TRUE)) %>%
  filter(period <= 50) %>%
  ggplot() +
  theme_bw() +
  geom_line(aes(x = period, y = mean_acq), colour = "red") + # Acquirer return
  geom_line(aes(x = period, y = mean_tar), colour = "blue") + # Target return
  geom_line(aes(x = period, y = mean_strat), colour = "green") + # Portfolio 
  labs(title = "Return spread between Target and Acquirer narrows quickly",
       subtitle = "Mean Daily Returns of Targets, Acquirers and Strategy per Day from Announcement",
       y = "Daily Returns",
       x = "Day from initial investment") + 
  theme_economist_white()

Cumulative Return

# Cumulative return for acquirer
initial_acq_v2 <- acq_tar_v2 %>%
  filter(period == 0) %>%
  rename(initial_acq = close_acquirer) %>%
  select(acquirer, target, initial_acq) %>%
  distinct()

cum_acq_v2 <- left_join(acq_tar_v2, initial_acq_v2, by = c("acquirer", "target")) %>%
  mutate(cum_ret_acq = ifelse(period > 0, close_acquirer/initial_acq - 1, NA)) %>%
  group_by(period) %>%
  summarise(mean_cum_ret_acq = mean(cum_ret_acq, na.rm =TRUE)) %>%
  filter(period <= 50)
# Cumulative return for target
initial_tar_v2 <- acq_tar_v2 %>%
  filter(period == 0) %>%
  rename(initial_tar = close_target) %>%
  select(acquirer, target, initial_tar)

cum_tar_v2 <- left_join(acq_tar_v2, initial_tar_v2, by = c("acquirer", "target")) %>%
  mutate(cum_ret_tar = ifelse(period > 0, close_target/initial_tar - 1, NA)) %>%
  group_by(period) %>%
  summarise(mean_cum_ret_tar = mean(cum_ret_tar, na.rm =TRUE)) %>%
  filter(period <= 50)
# Combine all
cum_all_v2 <- left_join(cum_acq_v2, cum_tar_v2, by = "period")
  

ggplot(cum_all_v2) +
  
  geom_line(aes(x = period, y = mean_cum_ret_tar), colour = "blue") +
  geom_line(aes(x = period, y = mean_cum_ret_acq), colour = "red") +
  theme_bw() +
  labs(title = "Mean Cumulative Return",
       subtitle = "Investments start 1 day after announcement of potential M&A deal",
       y = "Cumulative Return",
       x = "Day from initial investment")

Correlation between return and deal completion

Correlation between acquirer return and deal completion

end_acq_v2 <- acq_tar_v2 %>%
  mutate(diff = close_date - date) %>%
  filter(diff == 0) %>%
  rename(end_acq = close_acquirer) %>%
  select(acquirer, period, target, end_acq, DealStatus) %>%
  distinct()


deal_ret_acq_v2 <- left_join(end_acq, initial_acq, by = c("acquirer", "target")) %>%
  filter(acquirer != "RTX") %>%
  mutate(annualised_ret = (end_acq/initial_acq)^(252/period) - 1) %>%
  group_by(DealStatus) %>%
  summarise(mean_annualised_acq_ret = mean(annualised_ret, na.rm = TRUE))

deal_ret_acq_v2
DealStatusmean_annualised_acq_ret
Completed0.0782
Failed-0.407 

Correlation between target return and deal completion

end_tar_v2 <- acq_tar_v2 %>%
  mutate(diff = close_date - date) %>%
  filter(diff == 0) %>%
  rename(end_tar = close_target) %>%
  select(acquirer, period, target, end_tar, DealStatus) %>%
  distinct()


deal_ret_tar_v2 <- left_join(end_tar_v2, initial_tar_v2, by = c("acquirer", "target")) %>%
  filter(acquirer != "RTX") %>%
  mutate(annualised_ret = (end_tar/initial_tar)^(252/period) - 1) %>%
  group_by(DealStatus) %>%
  summarise(mean_annualised_tar_ret = mean(annualised_ret, na.rm = TRUE))

deal_ret_tar
DealStatusmean_annualised_tar_ret
Completed0.09
Failed-0.17

Returns of strategy over timeline

Using S&P 500 index if there is no deal

acq_tar2_v2 <- acq_tar_v2 %>%
  group_by(date) %>%
  summarise(ret_strat = mean(ret_combined))

SP_initial_v2 <- benchmark %>%
  filter(description == "SP_500") %>%
  filter(date >= "2014-05-01") %>%
  arrange(date) %>%
  head(n = 1) %>%
  rename(initial_index = close) %>%
  select(- date, - index_return)

benchmark %>%
  filter(description == "SP_500") %>%
  arrange(date) %>%
  left_join(SP_initial_v2, by = c("description", "index")) %>%
  left_join(acq_tar2_v2, by = "date") %>%
  select(date, close, initial_index, ret_strat) %>%
  mutate(index_ret = close/lag(close) - 1,
         cum_index_ret = close/initial_index,
         ret_strat_adjusted = ifelse(is.na(ret_strat), index_ret, ret_strat)) %>%
  filter(date >= "2014-05-01") %>%
  mutate(retplus1 = ret_strat_adjusted + 1,
    cum_ret_strat = cumprod(retplus1)) %>%
  ggplot() +
  geom_line(aes(x = date, y = cum_index_ret), colour = "red") +
  geom_line(aes(x = date, y = cum_ret_strat), colour = "green") ###?????###

Using risk-free rate if there is no deal

benchmark %>%
  filter(description == "SP_500") %>%
  arrange(date) %>%
  left_join(SP_initial_v2, by = c("description", "index")) %>%
  left_join(acq_tar2_v2, by = "date") %>%
  left_join(tbill, by = "date") %>%
  select(date, close, initial_index, ret_strat, T_bill_d) %>%
  mutate(index_ret = close/lag(close) - 1,
         cum_index_ret = close/initial_index,
         ret_strat_adjusted = ifelse(is.na(ret_strat), T_bill_d, ret_strat)) %>%
  filter(date >= "2014-05-01") %>%
  mutate(retplus1 = ret_strat_adjusted + 1,
    cum_ret_strat = cumprod(retplus1)) %>%
  ggplot() +
  geom_line(aes(x = date, y = cum_index_ret), colour = "red") +
  geom_line(aes(x = date, y = cum_ret_strat), colour = "green") ###?????###

CAPM

CAPM_v2 <- acq_tar_v2 %>%
  left_join(tbill, by = "date") %>%
  left_join(benchmarkSP, by = "date") %>%
  mutate(Rm_Rf = SP_500 - T_bill_d,
         Rs_Rf = ret_combined - T_bill_d) %>%
  drop_na(Rm_Rf, Rs_Rf) %>%
  filter(!is.infinite(Rs_Rf))

ggplot(CAPM_v2, aes(x = Rm_Rf, y = Rs_Rf, na.rm = TRUE)) +
  geom_point() 

CAPM_regression_v2 <- lm(Rs_Rf ~ Rm_Rf, data = CAPM, na.rm =TRUE)

CAPM_regression_v2
## 
## Call:
## lm(formula = Rs_Rf ~ Rm_Rf, data = CAPM, na.rm = TRUE)
## 
## Coefficients:
## (Intercept)        Rm_Rf  
##    0.005822     0.000526
huxreg(CAPM_regression_v2,
       statistics = c('#observations' = 'nobs', 
                      'R squared' = 'r.squared', 
                      'Adj. R Squared' = 'adj.r.squared', 
                      'Residual SE' = 'sigma'), 
       bold_signif = 0.05, 
       stars = NULL
)
(1)
(Intercept)0.006 
(0.003)
Rm_Rf0.001 
(0.311)
#observations2213     
R squared0.000 
Adj. R Squared-0.000 
Residual SE0.139